AMERICAN OPTION PRICING USING GENERALISED STOCHASTIC HYBRID SYSTEMS

Thispaperpresents a novel approach to pricing American options using piecewise diffusion Markov processes (PDifMPs), a generalised stochastic hybrid system combining continuous dynamics with discrete jumps. Standard models often assume constant drift and volatility, limiting their ability to capture the erratic nature of financial markets. Our method leverages PDifMPs to incorporate sudden market fluctuations, offering a more realistic asset price model. We benchmark our approach against the LongstaffSchwartz algorithm, including its modified version with PDifMP-based asset price trajectories. Numerical simulations show that the PDifMP method reflects market behaviour more accurately while enhancing computational eff iciency. The results suggest that PDifMPs significantly improve American options pricing by aligning with real-world stochastic volatility and market jumps, providing a more predictive and efficient approach.